{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b698a0c8",
   "metadata": {},
   "source": [
    "<center> <h1>MACHINE LEARNING APPRENTISSAGE AUTOMAITQIE</h1></center>\n",
    "<center> <h2>DEVOIR 1 </h2></center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a031183",
   "metadata": {},
   "source": [
    "\n",
    "a.\tEn utilisant la régression linéaire sur l'ensemble de données du tableau ci-dessous, prédire les ventes mensuelles compte tenu du coût de la publicité en ligne (sur le web) en trouvant l'équation de la ligne qui correspond à ce modèle. \n",
    " \n",
    "(𝑦=𝑏1𝑥+𝑏0): \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3064b602",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>广告费用</th><th scope=col>月销售额</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 500</td><td>200</td></tr>\n",
       "\t<tr><td>5000</td><td>900</td></tr>\n",
       "\t<tr><td>1900</td><td>450</td></tr>\n",
       "\t<tr><td>3200</td><td>680</td></tr>\n",
       "\t<tr><td>2000</td><td>490</td></tr>\n",
       "\t<tr><td>1000</td><td>300</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{ll}\n",
       " 广告费用 & 月销售额\\\\\n",
       " <int> & <int>\\\\\n",
       "\\hline\n",
       "\t  500 & 200\\\\\n",
       "\t 5000 & 900\\\\\n",
       "\t 1900 & 450\\\\\n",
       "\t 3200 & 680\\\\\n",
       "\t 2000 & 490\\\\\n",
       "\t 1000 & 300\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| 广告费用 &lt;int&gt; | 月销售额 &lt;int&gt; |\n",
       "|---|---|\n",
       "|  500 | 200 |\n",
       "| 5000 | 900 |\n",
       "| 1900 | 450 |\n",
       "| 3200 | 680 |\n",
       "| 2000 | 490 |\n",
       "| 1000 | 300 |\n",
       "\n"
      ],
      "text/plain": [
       "  广告费用 月销售额\n",
       "1  500     200     \n",
       "2 5000     900     \n",
       "3 1900     450     \n",
       "4 3200     680     \n",
       "5 2000     490     \n",
       "6 1000     300     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data4.9=read.csv(\"data.csv\", head = TRUE)\n",
    "lm4.9=lm(月销售额~广告费用,data4.9)#建立回归方程\n",
    "data4.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7c275e2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = 月销售额 ~ 广告费用, data = data4.9)\n",
       "\n",
       "Residuals:\n",
       "      1       2       3       4       5       6 \n",
       "-28.395 -28.709   3.729  31.416  28.167  -6.208 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 1.506e+02  2.190e+01   6.877  0.00234 ** \n",
       "广告费用    1.556e-01  8.077e-03  19.269 4.28e-05 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 29.42 on 4 degrees of freedom\n",
       "Multiple R-squared:  0.9893,\tAdjusted R-squared:  0.9867 \n",
       "F-statistic: 371.3 on 1 and 4 DF,  p-value: 4.275e-05\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm4.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "03815dbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data4.9)\n",
    "abline(lm4.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0631b52",
   "metadata": {},
   "source": [
    "*Réponse:* \n",
    "\n",
    "*y=1.556e-01x+1.506e+02*\n",
    "\n",
    "*y=0.1556x+150.6*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de01af46",
   "metadata": {},
   "source": [
    "#### b.\tVous avez formé un modèle de classificateur binaire qui donne une très grande précision sur les données de formation, mais une précision beaucoup plus faible sur les données de test. Choisissez les scénarios où cela peut être vrai : \n",
    " \n",
    "*(a)\tIl s'agit d'un exemple de surajustement (overfitting). *\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "907124ed",
   "metadata": {},
   "source": [
    "#### c.\tLa descente de gradient par lots effectue plus de calculs en mise à jour que la descente de gradient stochastique. \n",
    "*Réponse: a. Vrai*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77281193",
   "metadata": {},
   "source": [
    "#### d.\tDans un modèle de régression linéaire simple défini par la droite de prédiction y=-2x+0,5, on nous donne un ensemble de trois points de données et leurs vraies étiquettes : Ensemble =(x,y)=[(-1,-3),(1,3.4), (2,5.5)] \n",
    "\n",
    "Trouver la somme de l'erreur quadratique pour ce modèle ? \n",
    "\n",
    "\n",
    "Answer: original points:(-1，-3)，(1，3.4)，(2，5.5)\n",
    "points on the line :(-1，2.5)，(1，-1.5)，(2，-3.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "501e6353",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "135.26"
      ],
      "text/latex": [
       "135.26"
      ],
      "text/markdown": [
       "135.26"
      ],
      "text/plain": [
       "[1] 135.26"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(-3-2.5)^2+(3.4-(-1.5))^2+(5.5-(-3.5))^2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "694e562c",
   "metadata": {},
   "source": [
    "la somme de l'erreur quadratique: *135.26*"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "dfe3880f",
   "metadata": {},
   "source": [
    "#### 5. Pour prédire les échantillons dans la figure ci-dessous, quel modèle est le meilleur : régression logistique ou régression linéaire ? Expliquer pourquoi.\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02379501",
   "metadata": {},
   "source": [
    "*Réponse: régression linéaire, parce que ces points peuvent être facilement séparés par une ligne droite.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26dd6ed2",
   "metadata": {},
   "source": [
    "#### Que diriez-vous si nous changeons l'étiquette du point (0,1) de \"+\" à \"-\", expliquez pourquoi ? "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c4ac3ff",
   "metadata": {},
   "source": [
    "*Réponse: régression logique, parce que ces points ne peuvent pas être bien séparés par une ligne droite.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a44dde4f",
   "metadata": {},
   "source": [
    "#### 5. La figure ci-dessous montre la limite de deux modèles, quelle figure montre la limite après l'utilisation de la régression logistique ? \n",
    "\n",
    "*Réponse La figure (b) est la limite après régression logique parce que la figure (b) est une courbe*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df3dc54c",
   "metadata": {},
   "source": [
    "### Probabilités: \n",
    "\n",
    "##### Si la réalisation d’un événement A n’est pas influencée par celle d’un événement B, et inversement, A et B sont des événements incompatibles. \t \n",
    "*Faux*\n",
    "##### Si l’événement A est inclus dans l’événement B, la probabilité de A est supérieure à celle de B. \t \n",
    "*Faux*\n",
    "##### Si deux variables aléatoires sont indépendantes, la covariance entre ces variables est nécessairement nulle. \t \n",
    "*Vrai*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc65c6e4",
   "metadata": {},
   "source": [
    "#### 2.\tQue vaut p (A ∩ B), lorsque A et B sont :\n",
    "\n",
    "• incompatibles? *0*\n",
    "\n",
    "• independents? *p(A)*p(B)*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "325ff7d4",
   "metadata": {},
   "source": [
    "#### 3.\tOn suppose que les probabilités de divers éléments se présentent selon le tableau ci- dessous, les événements A, B, C d’une part et D et E d’autre part, étant incompatibles.\n",
    "\n",
    "##### a.\tReporter sur le tableau les probabilités manquantes.\n",
    "\n",
    "<!DOCTYPE html>\n",
    "<html lang=\"en\">\n",
    "<head>\n",
    "    <meta charset=\"UTF-8\">\n",
    "    <title></title>\n",
    "</head>\n",
    "<body>\n",
    "<table border=\"solid\">\n",
    "    <tr>\n",
    "        <td></td>\n",
    "        <td>A</td>\n",
    "        <td>B</td>\n",
    "        <td>C</td>\n",
    "        <td>total</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>D</td>\n",
    "        <td>0.08</td>\n",
    "        <td>0.36</td>\n",
    "        <td>0.16</td>\n",
    "        <td>0.60</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>E</td>\n",
    "        <td>0.32</td>\n",
    "        <td>0.04</td>\n",
    "        <td>0.04</td>\n",
    "        <td></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>Total</td>\n",
    "        <td>0.04</td>\n",
    "        <td>0.40</td>\n",
    "        <td>0.20</td>\n",
    "        <td>1</td>\n",
    "    </tr>\n",
    "</table>\n",
    "</body>\n",
    "</html>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f044ffee",
   "metadata": {},
   "source": [
    "b. *P(C)=0.16 p(C')=0.84 p(C' ∩ A)=0.08*\n",
    "\n",
    "c. *p(D)=0.08;  p(C\\ D)=0.04; p(C U D )=0.64.*"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
